A POCS-based graph matching algorithm

A novel projections onto convex sets (POCS) graph matching algorithm is presented. Two-way assignment constraints are enforced without using elaborate penalty terms, graduated nonconvexity, or sophisticated annealing mechanisms to escape from poor local minima. Results indicate that the presented algorithm is robust and compares favorably to other well-known algorithms.     

三维图匹配算法

目的 现有的图匹配算法大多应用于二维图像,对三维图像的特征点匹配存在匹配准确率低和计算速度慢等问题。为解决这些问题,本文将分解图匹配算法扩展应用在了三维图像上。方法 首先将需要匹配的两个三维图像的特征点作为图的节点集;再通过Delaunay三角剖分算法,将三维特征点相连,则相连得到的边就作为图的边集,从而建立有向图;然后,根据三维图像的特征点构建相应的三维有向图及其邻接矩阵;再根据有向图中的节点特征和边特征分别构建节点特征相似矩阵和边特征相似矩阵;最后根据这两个特征矩阵将节点匹配问题转化为求极值问题并求解。结果 实验表明,在手工选取特征点的情况下,本文算法对相同三维图像的特征点匹配有97.56%的平均准确率;对不同三维图像特征点匹配有76.39%的平均准确率;在三维图像有旋转的情况下,有90%以上的平均准确率;在特征点部分缺失的情况下,平均匹配准确率也能达到80%。在通过三维尺度不变特征变换（SIFT）算法得到特征点的情况下,本文算法对9个三维模型的特征点的平均匹配准确率为98.78%。结论 本文提出的基于图论的三维图像特征点匹配算法,经实验结果验证,可以取得较好的匹配效果。     

A graduated assignment algorithm for graph matching

A graduated assignment algorithm for graph matching is presented which is fast and accurate even in the presence of high noise. By combining graduated nonconvexity, two-way (assignment) constraints, and sparsity, large improvements in accuracy and speed are achieved. Its low order computational complexity [O(lm), where l and m are the number of links in the two graphs] and robustness in the presence of noise offer advantages over traditional combinatorial approaches. The algorithm, not restricted to any special class of graph, is applied to subgraph isomorphism, weighted graph matching, and attributed relational graph matching. To illustrate the performance of the algorithm, attributed relational graphs derived from objects are matched. Then, results from twenty-five thousand experiments conducted on 100 mode random graphs of varying types (graphs with only zero-one links, weighted graphs, and graphs with node attributes and multiple link types) are reported. No comparable results have been reported by any other graph matching algorithm before in the research literature. Twenty-five hundred control experiments are conducted using a relaxation labeling algorithm and large improvements in accuracy are demonstrated     

迭代的图变换匹配算法

目的：图像的精确匹配在图像处理与识别中起着重要的作用。为了提高图像的匹配效果,本文提出了一种迭代的图变换匹配算法来实现误匹配关系的去除从而提高图像的匹配精度。方法：该算法首先利用传统的图变换匹配(GTM)算法从初始匹配关系集合中获得较为精确的匹配关系子集,然后,利用已经获得的正确匹配点集与初始匹配点集之间的几何关系对初始匹配进行修正。最后,利用GTM对修正后的匹配关系进一步优化,从而得到更多的精确匹配关系。结果：实验结果显示在不同的图像变换场景下,相比于传统GTM算法,该算法具有较高的查全率。结论：所提算法能够克服传统GTM算法所得正确匹配关系少的缺陷。     

A parallel algorithm for graph matching and its MasParimplementation

Search of discrete spaces is important in combinatorial optimization. Such problems arise in artificial intelligence, computer vision, operations research, and other areas. For realistic problems, the search spaces to be processed are usually huge, necessitating long computation times, pruning heuristics, or massively parallel processing. We present an algorithm that reduces the computation time for graph matching by employing both branch-and-bound pruning of the search tree and massively-parallel search of the as-yet-unpruned portions of the space. Most research on parallel search has assumed that a multiple-instruction-stream/multiple-data-stream (MIMD) parallel computer is available. Since massively parallel stream (SIMD) computers are much less expensive than MIMD systems with equal numbers of processors, the question arises as to whether SIMD systems can efficiently handle state-space search problems. We demonstrate that the answer is yes, and in particular, that graph matching has a natural and efficient implementation on SIMD machines     

基于图匹配的旋转不变弹性点匹配算法

针对旋转不变的弹性点匹配问题,提出一种基于图匹配的算法。对两点集分别构造边集合,然后定向的形状上下文距离和边长度的差别被用于度量两点集的边之间的相似性。基于边的相似性,点对应关系通过求解一个图匹配问题而恢复。实验结果表明该算法可以获得很好的配准结果并且鲁棒、高效。     

一种基于图割理论的快速立体匹配算法

针对传统的立体匹配算法中存在的低纹理区域和遮挡区域匹配精度低、实时性不好等问题,提出了一种基于图割理论的立体匹配算法.把图像分割成色彩单一的不同区域;计算初始视差图,利用可靠点求取各分割区域的平面模板参数,对模板参数相同的相邻区域进行融合;构造全局能量函数,采用图割算法求取全局能量最小的视差最优分配.实验结果表明,该算法对低纹理区域和遮挡区域均有较好的匹配结果,能够满足高精度、高实时性的要求.     

A (sub)graph isomorphism algorithm for matching large graphs

We present an algorithm for graph isomorphism and subgraph isomorphism suited for dealing with large graphs. A first version of the algorithm has been presented in a previous paper, where we examined its performance for the isomorphism of small and medium size graphs. The algorithm is improved here to reduce its spatial complexity and to achieve a better performance on large graphs; its features are analyzed in detail with special reference to time and memory requirements. The results of a testing performed on a publicly available database of synthetically generated graphs and on graphs relative to a real application dealing with technical drawings are presented, confirming the effectiveness of the approach, especially when working with large graphs.     

A subgraph matching algorithm based on subgraph index for knowledge graph

The problem of subgraph matching is one fundamental issue in graph search, which is NP-Complete problem. Recently, subgraph matching has become a popular research topic in the field of knowledge graph analysis, which has a wide range of applications including question answering and semantic search. In this paper, we study the problem of subgraph matching on knowledge graph. Specifically, given a query graph q and a data graph G, the problem of subgraph matching is to conduct all possible subgraph isomorphic mappings of q on G. Knowledge graph is formed as a directed labeled multi-graph having multiple edges between a pair of vertices and it has more dense semantic and structural features than general graph. To accelerate subgraph matching on knowledge graph, we propose a novel subgraph matching algorithm based on subgraph index for knowledge graph, called as F G q_T-Match. The subgraph matching algorithm consists of two key designs. One design is a subgraph index of matching-driven flow graph ( F G q_T), which reduces redundant calculations in advance. Another design is a multi-label weight matrix, which evaluates a near-optimal matching tree for minimizing the intermediate candidates. With the aid of these two key designs, all subgraph isomorphic mappings are quickly conducted only by traversing F G q_T. Extensive empirical studies on real and synthetic graphs demonstrate that our techniques outperform the state-of-the-art algorithms.     

An improved graph cut algorithm in stereo matching

In stereo matching tasks, the matching effect is often very poor when the texture of the region is weak or repeated. To solve this problem, an improved Graph Cut stereo matching algorithm based on Census transform is proposed. The Hamming distance of the corresponding pixels in the left and right images after Census transform is introduced as the similarity measure in the data term of the energy function. In this way, the dependence on the pixel value is reduced. The stereo matching experiments are implemented on the standard images of Middlebury stereo benchmark and the real scene images, and it demonstrates that our algorithm is robust and can obtain better performance in weak texture or repeated texture region.     

A genetic algorithm and its parallelization for graph matching with similarity measures

Graph matching and similarity measures of graphs have many applications to pattern recognition, machine vision in robotics, and similarity-based approximate reasoning in artificial intelligence. This paper proposes a method of matching and a similarity measure between two directed labeled graphs. We define the degree of similarity, the similar correspondence, and the similarity map which denotes the matching between the graphs. As an approximate computing method, we apply genetic algorithms (GA) to find a similarity map and compute the degree of similarity between graphs. For speed, we make parallel implementations in almost all steps of the GA. We have implemented the sequential GA and the parallel GA in C programs, and made simulations for both GAs. The simulation results show that our method is efficient and useful. This work was presented, in part, at the Second International Symposium on Artificial Life and Robotics, Oita Japan, February 18–20, 1997     

图谱和Kuhn-Munkres算法在图匹配中的应用研究

为了对图数据库中的结构化数据进行有效的匹配分析,提出了基于全局结构相似度以及节点位置相似度的Kuhn-Munkres算法。首先对图数据构建全局以及节点位置矩阵,全局相似度矩阵用邻接矩阵的拉普拉斯谱特征构造,位置相似度矩阵首先使用高斯核函数进行节点相对位置的归一化计算,再利用其谱特征构造。节点位置相似度主要描述图所有节点之间的相对位置,弥补了全局结构相似度只刻画图整体结构的不足。最后使用Kuhn-Munkres算法进行图匹配,得到二分图的最大权匹配。实验表明,改进的Kuhn-Munkres算法有效提高了节点之间的匹配正确率。     

一种改进的基于图割的立体匹配算法

为了提高立体匹配算法的精确度,提出了一种结合图割与Mean Shift图像分割的立体匹配算法。首先用Mean Shift算法对参考图像进行图像分割,得到分割后的标记图,然后将分割信息结合到图割算法的能量函数中,最后用改进的能量函数和图割算法得出致密的视差图。实验结果表明,提出的算法具有更高的精确度和更好的边缘特征。     

基于二分图的故障规则匹配优化算法

针对传统的基于相似度的故障规则匹配方法中未考虑输入条件与规则前件的整体匹配程度问题,采用二分图最优匹配方法对匹配过程进行优化,提出一种基于二分图的故障规则匹配优化算法,并将其应用于故障诊断推理．实例分析表明,与其他相似度匹配算法相比,所提出的方法有效提高了规则匹配的准确率,而且降低了时间消耗．     

An efficient parallel graph edge matching algorithm and its applications

A fast and efficient parallel algorithm for finding a maximal edge matching in an undirected graphG(V,E) is proposed.It runs in O(log n)time with O(m,/log n n)processors on an EREW PRAM for a class of graph set П,where n=|V|,m=|E|and П includes at least (i)planar graphs;(ii) graphs of bounded genus;and (iii)graphs of bounded maximum degress and so on.Our algorithm improves the previously known best algorithms by a factor of logn in the time complexity with linear number of processors on EREW PRAMs when the input is limited to П.     

一种基于SSD和图割的快速立体匹配算法

针对图割法的立体匹配算法耗时多的问题,提出了一种基于S S D和图割的快速立体匹配算法。为了缩小视差搜索范围,缩短匹配时间,先采用区域匹配S S D算法得到初始视差,然后再采用左右一致性校验法去除误匹配点,可以提高初始视差图的质量;在构造能量函数时,把初始视差图中的像素视差作为图割的能量函数的限制项,根据这些限制可以减少不必要的节点,从而减少了计算量,缩短匹配时间。通过实验证明了本文算法在保证匹配图像质量的情况下,能提高匹配效率,减少匹配时间。     

Structural graph matching using the EM algorithm and singular valuedecomposition

This paper describes an efficient algorithm for inexact graph matching. The method is purely structural, that is, it uses only the edge or connectivity structure of the graph and does not draw on node or edge attributes. We make two contributions: 1) commencing from a probability distribution for matching errors, we show how the problem of graph matching can be posed as maximum-likelihood estimation using the apparatus of the EM algorithm; and 2) we cast the recovery of correspondence matches between the graph nodes in a matrix framework. This allows one to efficiently recover correspondence matches using the singular value decomposition. We experiment with the method on both real-world and synthetic data. Here, we demonstrate that the method offers comparable performance to more computationally demanding methods     

A new graph matching method for point-set correspondence using the EM algorithm and Softassign

Finding correspondences between two point-sets is a common step in many vision applications (e.g., image matching or shape retrieval). We present a graph matching method to solve the point-set correspondence problem, which is posed as one of mixture modelling. Our mixture model encompasses a model of structural coherence and a model of affine-invariant geometrical errors. Instead of absolute positions, the geometrical positions are represented as relative positions of the points with respect to each other. We derive the Expectation–Maximization algorithm for our mixture model. In this way, the graph matching problem is approximated, in a principled way, as a succession of assignment problems which are solved using Softassign. Unlike other approaches, we use a true continuous underlying correspondence variable. We develop effective mechanisms to detect outliers. This is a useful technique for improving results in the presence of clutter. We evaluate the ability of our method to locate proper matches as well as to recognize object categories in a series of registration and recognition experiments. Our method compares favourably to other graph matching methods as well as to point-set registration methods and outlier rejectors.